Considering the detailed dynamical behavior that we obtain, the \(\beta >0.5\)  exponent value observed for the random deposition-like regime of our 1D fronts at early times might be anticipating the singular behavior that arises in higher dimensions. Recall that the 1D tensionless KPZ equation proper features \(\beta =1/2\)  at early, preasymptotic times [1]}, while larger values of \(\beta \)  are usually taken as indicative of morphological instabilities for systems with time-dependent noise, as \(\beta =1/2\)  characterizes the roughness increase for the random deposition process [2]}.
